Interferometer for determining characteristics of an object surface, including processing and calibration

ABSTRACT

Disclosed is a system including: (i) an interferometer configured to direct test electromagnetic radiation to a test surface and reference electromagnetic radiation to a reference surface and subsequently combine the electromagnetic radiation to form an interference pattern, the electromagnetic radiation being derived from a common source; (ii) a multi-element detector; (iii) one or more optics configured to image the interference pattern onto the detector so that different elements of the detector correspond to different illumination angles of the test surface by the test electromagnetic radiation; and (iv) an electronic processor coupled to the detector, wherein the electronic processor is configured to process information measured by the detector to determine information about a test object having the test surface. The measurements made by the detector elements provide ellipsometry/reflectometry data for the test surface.

CROSS-REFERENCE TO RELATED APPLICATIONS

Under 35 U.S.C § 119(e), the present application claims priority to U.S.Provisional Patent Application Ser. No. 60/645,448, filed Jan. 20, 2005and entitled “INTERFEROMETER FOR DETERMINING CHARACTERISTICS OF ANOBJECT SURFACE,” the contents of which is incorporated herein byreference.

BACKGROUND

The invention relates to interferometry.

Interferometric techniques are commonly used to measure the profile of asurface of an object. To do so, an interferometer combines a measurementwavefront reflected from the surface of interest with a referencewavefront reflected from a reference surface to produce aninterferogram. Fringes in the interferogram are indicative of spatialvariations between the surface of interest and the reference surface.

A scanning interferometer scans the optical path length difference (OPD)between the reference and measurement legs of the interferometer over arange comparable to, or larger than, the coherence length of theinterfering wavefronts, to produce a scanning interferometry signal foreach camera pixel used to measure the interferogram. A limited coherencelength can be produced, for example, by using a white-light source,which is referred to as scanning white light interferometry (SWLI). Atypical scanning white light interferometry (SWLI) signal is a fewfringes localized near the zero optical path difference (OPD) position.The signal is typically characterized by a sinusoidal carrier modulation(the “fringes”) with bell-shaped fringe-contrast envelope. Theconventional idea underlying SWLI metrology is to make use of thelocalization of the fringes to measure surface profiles.

SWLI processing techniques include two principle trends. The firstapproach is to locate the peak or center of the envelope, assuming thatthis position corresponds to the zero optical path difference (OPD) of atwo-beam interferometer for which one beam reflects from the objectsurface. The second approach is to transform the signal into thefrequency domain and calculate the rate of change of phase withwavelength, assuming that an essentially linear slope is directlyproportional to object position. See, for example, U.S. Pat. No.5,398,113 to Peter de Groot. This latter approach is referred to asFrequency Domain Analysis (FDA).

Scanning interferometry can be used to measure surface topography and/orother characteristics of objects having complex surface structures, suchas thin film(s), discrete structures of dissimilar materials, ordiscrete structures that are underresolved by the optical resolution ofan interference microscope. Such measurements are relevant to thecharacterization of flat panel display components, semiconductor wafermetrology, and in-situ thin film and dissimilar materials analysis. See,e.g., U.S. Patent Publication No. US-2004-0189999-A1 by Peter de Grootet al. entitled “Profiling Complex Surface Structures Using ScanningInterferometry” and published on Sep. 30, 2004, the contents of whichare incorporated herein by reference, and U.S. Patent Publication No.US-2004-0085544-A1 by Peter de Groot entitled “Interferometry Method forEllipsometry, Reflectometry, and Scatterometry Measurements, IncludingCharacterization of Thin Film Structures” and published on May 6, 2004,the contents of which are incorporated herein by reference.

Other techniques for optically determining information about an objectinclude ellipsometry and reflectometry. Ellipsometry determines complexreflectivity of a surface when illuminated at an oblique angle, e.g.60°, sometimes with a variable angle or with multiple wavelengths. Toachieve greater resolution than is readily achievable in a conventionalellipsometer, microellipsometers measure phase and/or intensitydistributions in the back focal plane of the objective, also known asthe pupil plane, where the various illumination angles are mapped intofield positions. Such devices are modernizations of traditionalpolarization microscopes or “conoscopes,” linked historically tocrystallography and mineralogy, which employs crossed polarizers and aBertrand lens to analyze the pupil plane birefringent materials.

Conventional techniques used for thin film characterization (e.g.,ellipsometry and reflectometry) rely on the fact that the complexreflectivity of an unknown optical interface depends both on itsintrinsic characteristics (material properties and thickness ofindividual layers) and on three properties of the light that is used formeasuring the reflectivity: wavelength, angle of incidence, andpolarization state. In practice, characterization instruments recordreflectivity fluctuations resulting from varying these parameters overknown ranges. Optimization procedures such as least-squares fits arethen used to get estimates for the unknown parameters by minimizing thedifference between measured reflectivity data and a reflectivityfunction derived from a model of the optical structure.

SUMMARY

In at least one embodiment, an interferometry method and apparatus isdisclosed that produces angularly resolved interference signals from atest surface over a range of wavelenghths. The information related toeach wavelength may be extracted mathematically or in hardware.Furthermore, the optical hardware for obtaining the angularly resolvedinterference signals from the test surface is interchangeable withoptical hardware useful for other surface characterization tasks, suchas conventional interferometric surface profiling. Accordingly, aninterferometry system is disclosed that is capable of operating in anellipsometry mode for providing complex reflectivity information of thetest surface for a range of angles, wavelengths, and polarizations, anda profiling mode for providing information about the test surface over arange of test surface locations.

We now summarize various aspects and features of the invention.

In general, in one aspect, the system includes: (i) an interferometerconfigured to direct test electromagnetic radiation to a test surfaceand reference electromagnetic radiation to a reference surface andsubsequently combine the electromagnetic radiation to form aninterference pattern, the electromagnetic radiation being derived from acommon source; (ii) a multi-element detector; and (iii) one or moreoptics configured to image the interference pattern onto the detector sothat different elements of the detector correspond to differentillumination angles of the test surface by the test electromagneticradiation.

Embodiments of the system may include any of the following features.

The interferometer may include an interference objective having a pupilplane. Furthermore, the one or more optics may image the interferencepattern at the pupil plane to the multi-element detector. Also, theinterferometer may be configured to image EM radiation emitted from thecommon source to the pupil plane of the interference objective. By wayof example, the interference objective be a Mirau objective or aMichelson objective.

The one or more optics may be configured to be selective adjusted toimage the test surface onto the detector or to image the interferencepattern onto the detector so that different elements of the detectorcorrespond to different illumination angles of the test surface by thetest electromagnetic radiation. In other words, the detector in thesystem can alternate between recording an optical profile of the testsurface and recording angularly resolved interference data about thetest surface.

In some embodiments, the test EM radiation can be reflected from thetest surface. Alternatively, in other embodiments, the test EM radiationcan be transmitted through the test surface.

The interferometer may include a scanning stage to adjust the relativeoptical path length between the test and reference EM radiation whenthey form the optical interference pattern.

The system may further include the common source. For example, thecommon source may be a broadband source. The interferometer may alsoinclude a scanning stage to adjust the relative optical path lengthbetween the test and reference EM radiation when they form the opticalinterference pattern, and the scanning stage may be configured to varythe optical path length over a range larger than a coherence length forthe common source.

The interferometer may further include one or more polarization elementspositioned to adjustably control the polarization content of theinterference pattern measured by the detector

The system may further include an electronic processor coupled to thedetector, wherein the electronic processor is configured to analyzeinformation about the interference pattern to determine angularlyresolved information about a test object having the test surface. Forexample, the test object may have at least one layer adjacent the testsurface.

In general, in another aspect, an apparatus is disclosed including: (i)an interferometer configured to direct test light to a test surface andsubsequently combine it with reference light to form an interferencepattern, the test and reference light being derived from a commonsource; (ii) an electronic detector; and (iii) one or more opticsconfigured to direct at least a portion of the combined light to thedetector so that different regions of the detector correspond todifferent illumination angles of the test surface by the test light.

Embodiments of the apparatus may include any of the following features.

The interferometer may include a beam splitter configured to separateinput light derived from the common source into the test light and thereference light, and a reference surface positioned to reflect thereference light before it is combined with the test light. The testlight is configured to reflect from the test surface, and the beamsplitter in the interferometer is positioned to recombine the test andreference light after they reflect from the respective test andreference surfaces.

The interferometer may further includes a lens to focus the test lightto the test surface. The lens defines a pupil plane and the one or moreoptics image the pupil plane onto the detector. The common source isspatially extended, and the input light is imaged from the common sourceto the pupil plane. A field stop can be positioned to define the spatialextent of the test light on the test surface.

The interferometer can include an interference objective having a pupilplane. For example, the interference objective can be a Mirauinterference objective or a Michelson interference objective. The one ormore optics can image the interference pattern at the pupil plane to themulti-element detector.

The detector can include multiple detector elements with differentdetector elements corresponding to different illumination angles of thetest surface by the test light.

The test and reference light derived from the common source can be inthe visible portion of the electromagnetic spectrum. Alternatively, theycan be in the ultraviolet, near-infrared, or infrared portions of theelectromagnetic spectrum.

The test light is configured to reflect from the test surface.Alternatively, in some embodiments, the test light is configured totransmit through the test surface.

The apparatus can further include a translation stage configured toadjust the relative optical path length between the test and referencelight when they form the interference pattern. For example, theapparatus can further include a base for supporting a test object havingthe test surface, and the translation stage can be configured to move atleast a portion of the interferometer (such as an interference objectivein the interferometer) relative to the base.

The apparatus can further include the common source. The translationstage can be configured to vary the optical path length over a rangelarger than a coherence length for the common source. The common sourcecan be a broadband source spanning more than 50 nm (or more than 100 nm,or even more than 200 nm) at full width half maximum.

In certain embodiments, the common source can be a tunable source. Forexample, the apparatus can further include an electronic processorcoupled to the detector and the tunable source, and configured toprocess images recorded by the detector for different wavelengthsettings of the tunable source. In such cases, the interferometer caninclude a reference surface positioned to reflect the reference light,wherein the reference surface is further positioned to produce anon-zero optical path length difference with the test light at theinterference pattern.

The interferometer can further include one or more polarization elementspositioned to adjust the polarization content of the interferencepattern measured by the detector. For example, the one or morepolarization elements can include a first polarizer positioned toreceive input light from the common source from which the test andreference light are derived. In one case, for example, the one or morepolarization element can further include a second polarizer positionedto receive the combined light before it reaches the detector. In anothercase, for example, the first polarizer is further positioned to receivethe combined light before it reaches the detector. Furthermore, the oneor more polarization elements can include a quarter-wave platepositioned to receive input light from the common source from which thetest and reference light are derived and the combined light before itreaches the detector.

The interferometer can include a lens to focus the test light to thetest surface, and the one or more polarization elements can include afirst polarizer positioned to cause the test light to be linearlypolarized prior to being focused by the lens. For example, the firstpolarizer can cause the test light to have a polarization at the testsurface that varies azimuthally between s- and p-polarized light. Thefirst polarizer can be positioned to also cause the combined light to belinearly polarized at the detector. Alternatively, the one or moreoptics can further include a second polarizer positioned to cause thecombined light to be linearly polarized at the detector. For example,the first and second polarizers can have a common orientation.

Different locations on the detector can correspond to differentcombinations of Fresnel reflection coefficients for s- and p-polarizedlight at the detector. The relative combination of the s- andp-polarized reflection coefficients can depend on an azimuthalcoordinate on the detector and the angle dependence of the Fresnelcoefficients depends on a radial coordinate.

The interferometer can include a beam splitter positioned receive inputlight from the common source along a first direction and direct thecombined light toward the detector along a second direction differentfrom the first direction.

The apparatus can further include an electronic processor coupled to thedetector, wherein the electronic processor is configured to processinformation measured by the detector to determine information about atest object having the test surface. For example, the test object canincludes one or more layers on a substrate. In certain embodiments, theelectronic processor can extract angularly resolved reflectivityinformation about the test surface from the detector measurement, anddetermine the information about the test object based on the angularlyresolved information. For example, the information can include arefractive index estimate for a portion of the test object and/or athickness estimate for a layer in the test object. The electronicprocessor can be configured to determine the information about the testobject based on a comparison between data based on the informationmeasured by the detector and a model for the test object. For example,the model can provide an estimate for the measured information as afunction of one or more parameters for the test object, and wherein thecomparison selects values for the one or more parameters to optimize thefit between the measured information and that provided by the model.

The apparatus can further include a translation stage configured toadjust the relative optical path length between the test and referencelight when they form the interference pattern, wherein the electronicprocessor is configured to analyze an interference intensity signalmeasured at each of multiple locations across the detector and producedby scanning the translation stage. Furthermore, the electronic processorcan be configured to determine the correspondence between the differentregions of the detector and the different illumination angles of thetest surface by the test light based on the frequency of the intensitysignal at different locations on the detector.

Also, the electronic processor can be configured to extract angularlyresolved and wavelength-resolved information about the test surfacebased on the intensity signals measured across the detector. Forexample, the electronic processor can be configured to transform theinterference signal at different locations of the detector into afrequency domain to extract the angularly resolved andwavelength-resolved information.

The interferometer can includes one or more polarization elementspositioned to adjust the polarization content of the interferencepattern measured by the detector. As a result, the electronic processorcan be configured to extract angularly resolved, wavelength-resolved,and polarization-resolved information about the test surface based onthe intensity signal measured across the detector. For example, theangularly resolved, wavelength-resolved, and polarization-resolvedinformation can be complex reflectivity information about the testsurface.

The electronic processor can be configured to select a subset of each ofthe interference intensity signals, the subsets corresponding to aselected interface in the test object, and process the subsets ofinterference intensity signals to determine information about the testobject related to the selected interface.

The electronic processor can store calibration information about theoptical properties of the interferometer and use the calibrationinformation and the information measured by the detector to determinethe information about the test object.

The apparatus can be configured to adjustably switch between a firstmode of operation in which the combined light is directed to thedetector so that different regions of the detector correspond todifferent illumination angles of the test surface by the test light anda second mode of operation in which different regions of the detectorcorrespond to the different regions of the test surface illuminated bythe test light to enable a profiling mode of operation.

For example, the apparatus can further include a stage configured toadjust the position of the detector relative to the one or more opticsto switch between the first and second modes of operation. The apparatuscan also include an electronic controller coupled to the detector stageand configured to adjustably cause the stage to switch between the firstand second modes of operation.

In another example, the one or more optics can include a first set ofone or more optics for operating in the first mode of operation and asecond set of one or more optics for operating in the second mode ofoperation. The apparatus can include a multi-position optics holdersupporting the first and second set of optics and configured toadjustably position one of the first and second sets and not the otherof the first and second sets in the path of the combined light beingdirected to the detector to switch between the first and second modes.

The multi-positioned lens holder can be motorized, and the apparatus canfurther include an electronic controller coupled to the motorizedmulti-position optics holder to selectively cause the multi-positionoptics holder to switch between the first and second modes of operation.

In yet another example, the apparatus can further include a second setof one or more optics, a beam splitter positioned to direct a firstportion of the combined to light to the first of optics and direct asecond portion of the combined light to the second set of optics, and asecond electronic detector. The second set of optics is configured todirect the second portion of the combined light to the second electronicdetector so that different regions of the second detector correspond tothe different regions of the test surface illuminated by the test light,corresponding to the second mode.

The apparatus can further include an electronic processor coupled to thedetector and configured to process information measured by the detectorin each mode of operation to determine information about a test objecthaving the test surface. The electronic processor is configured to useinformation derived in one mode of operation to assist in determiningfurther information about the test object when using the other mode ofoperation.

For example, the information derived in the first mode may correspond toa refractive index of a portion of the test object, and the electronicprocessor can be configured to determined a phase change on reflection(PCOR) based on the refractive index to assist in determining topographyinformation when operating in the second mode. In another example, theinformation derived in the second mode corresponds to an estimate forthe surface roughness of the test surface, and the electronic processorcan be configured to use the surface roughness estimate to processinformation measured by the detector in the first mode to determineinformation about the test object.

The interferometer can include a multi-position mount (e.g., a turret)configured to support multiple objectives and position a selectedobjective in the path of input light from the common source, themultiple objectives including at least one interference objective. Themulti-position mount can be motorized, and the apparatus can furtherinclude an electronic controller coupled to the multi-position mount toselectively cause the mount to switch between objectives. For example,the multiple objectives can include two different interferenceobjectives, only one of which includes a polarization optic. Themultiple objectives can also include one or more non-interferometricobjectives, each of which when positioned in the path of the input lightenables the apparatus to operate in a non-interferometric, microscopemode.

In general, in another aspect, an interferometry method is disclosed,including: (i) directing test light to a test surface over a range ofillumination angles; (ii) subsequently combining the test light withreference light to form an interference pattern, wherein the test andreference light are derived from a common source; and (iii) directing atleast a portion of the combined light to a multi-element detector sothat different elements of the detector correspond to differentillumination angles of the test surface by the test light.

Embodiments of the method may include any of the following features.

The combined light can be directed to the detector by imaging a pupilplane for the test light to the detector. The method may further includemeasuring an interference signal at each of multiple elements of thedetector as a function of varying an optical path length differencebetween the test and reference light.

The test light, reference light, and combined light can be selectivelypolarized.

The method can further include determining information about a testobject having the test surface based on a signal measured at differentdetector elements. For example, determining the information about thetest object can include determining a reflectivity for the test surfacewith respect to different illumination angles and wavelengths. Thereflectivity can be a complex reflectivity with respect to the differentillumination angles and wavelengths, for a selected polarization state.Determining the information about the test object further can includecomparing the measured reflectivity to an estimate for the reflectivitybased on a model of the test object.

As part of a calibration step, the method may further includedetermining a relationship between different illumination angles of thetest surface by the test light and different elements of the detectorbased on the frequency of the interference signal at different detectorelements. Also, the method may further include determining the locationof an optical axis for the combined light on the detector based on thefrequency of the interference signal at different detector elements.Also, the method may further include determining the rate at which theoptical path length difference is varied by based on the frequency ofthe interference signal at different detector elements.

As part of a further calibration, the test surface may have knownreflection properties, and the method may further include calibratingreflection parameters of an interferometer used to direct the test lightand combine it with the reference light based on a signal measured atdifferent detector elements and the known reflection parameters of thetest surface. The method may further include repeating the steps with asecond test surface having known reflection properties, and furthercalibrating reflection parameters of the interferometer based on signalsmeasured at the different detector elements and the known reflectionparameters of the test surfaces.

The method may further include features corresponding to those listedfor the apparatus described above.

In general, in another aspect, an apparatus is disclosed including: aninterferometry system configured to operate in each of a first mode thatmeasures reflectivity of a test surface over a range of angles andwavelengths and a second mode that measures one or more properties ofthe test surface over across a range of test surface locations.

Embodiments of the apparatus may include any of the following features.

The apparatus can be configured to selectively switch between the firstand second modes. Alternatively, the apparatus can be configured tosimultaneously provide measurements in both modes.

The interferometer can include at least one electronic detector, and inthe first mode different elements of the detector correspond todifferent illumination angles of the test surface by test light in theinterferometry system. The first mode can corresponds to an ellipsometrymode that measures the reflectivity of the test surface over the rangeof angles and wavelengths for one or more selected polarizations.Alternatively, the first mode can corresponds to an reflectometry modethat measures the reflectivity of the test surface over the range ofangles and wavelengths for unpolarized light. To operate in the firstmode, the interferometer can image a pupil plane for test light directedto the test surface to the detector.

In the second mode, different elements of the detector correspond todifferent locations of the test surface illuminated by test light in theinterferometry system. Specifically, the interferometer is configured toimage the test surface to the detector. The second mode can be aprofiling mode.

The apparatus can further include an electronic processor coupled to theinterferometry system and configured to process information measured bythe interferometry system in each mode of operation to determineinformation about a test object having the test surface. Furthermore, heelectronic processor can be configured to use information derived in onemode of operation to assist in determining further information about thetest object when using the other mode of operation.

The interferometry system can be further configured to selectivelyoperate in non-interferometric microscopy mode to measurenon-interferometric optical images of the test surface.

In general, in another aspect, a method is disclosed including: (i)using an interferometry system to measure a test surface in a first modeof operation that measures reflectivity of the test surface over a rangeof angles and wavelengths; and (ii) using the same interfometry systemto measure the test surface in a second mode of operation thatinterferometrically profiles a topography of the test surface.

The method may further include using the same interferometry system tomeasure the test surface in a third mode of operation that produces oneor more non-interferometric, microscope images of the test surface.

As used herein, “light” is not limited to electromagnetic radiation inthe visible spectral region, but rather refers generally toelectromagnetic radiation in any of the ultraviolet, visible, nearinfrared, and infrared spectral regions.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. In case of conflict with anydocument incorporated by reference, the present disclosure controls.

Other features, objects, and advantages of the invention will beapparent from the following detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of an interferometry system 100 configuredto operate in an ellipsometry mode.

FIG. 2 is a graph showing an example of an interferometry signalmeasured a detector element when the optical path length difference(“OPD”) between the test and reference light in interferometry system100 is varied, where the OPD is expressed by frame number.

FIG. 3 is a schematic diagram of interferometry system 100 reconfiguredto operate in a profiling mode.

FIG. 4 shows plots of a data collected by a detector element for a testobject having 1-micron thick silicon dioxide film on a siliconsubstrate. The left plot shows interferometry signal measured by thedetector element as a function of frame number during the OPD scan. Theright plot shows the Fourier transform of the interferometry signal withrespect to wavenumber, with spectral magnitude being shown by solidtrace and spectral phase being shown by the dotted trace.

FIG. 5 shows plots of experimentally derived, complex reflectivitycoefficients for a selected angle of incidence (43 degrees) and aselected wavelength (576 nm) as a function of azimuth angle for a 675-nmthick silicon dioxide monolayer film on a silicon substrate. The leftplot shows the spectral component Z (top curve being the real componentand the bottom curve being the imaginary component) and the right plotshows the corresponding values for z (top curve being the real componentand the bottom curve being the imaginary component), which scales Z withrespect to a system calibration.

FIG. 6 shows a plot of the interferometry signal for a 5-micron thickfilm of silicon dioxide on silicon to demonstrate how portion of thesignal can be selected to isolate a selected interface in the structure.

FIG. 7 is a schematic diagram of another embodiment for interferometrysystem 100.

FIG. 8 is a schematic diagram of yet another embodiment forinterferometry system 100.

FIG. 9 is a schematic diagram of interferometry system 100 showing howvarious components can be adjusted in an automated fashion under thecontrol an electronic processor.

Like reference numerals in different drawings refer to common elements.

DETAILED DESCRIPTION

Conventional techniques used for thin film characterization (e.g.,ellipsometry) rely on the fact that the complex reflectivity of anunknown optical interface depends both on its intrinsic characteristics(e.g., material properties and thicknesses of individual layers) and onthree properties of the light that is used for measuring thereflectivity: wavelength, angle of incidence, and polarization state. Inpractice, ellipsometry instruments record reflectivity fluctuationsresulting from varying these parameters over known ranges. Optimizationprocedures such as least-squares fits are then used to get estimates forthe unknown parameters by minimizing the difference between measuredreflectivity data and a reflectivity function derived from a model ofthe optical structure.

Embodiments disclosed herein provide an interferometry system and methodfor rapidly collecting a large number of reflectivity data points over awide range for all three optical characteristics of the probe beam(i.e., wavelength, angle of incidence, and polarization state) for aselected region of a test surface. Furthermore, the same instrument canswitch from this ellipsometry mode of operation to a profiling mode toprovide laterally resolved information about the test surface. Moreover,information determined in the ellipsometry mode can be used to improvethe accuracy of the information obtained in the profiling mode. Forexample, the ellipsometry mode can provide information about thematerial properties of the test object having the test surface to createmore accurate topography maps of the various optical interfaces, the topsurface (air interface), for example, being of particular interest.

Exemplary Apparatus

FIG. 1 is a schematic diagram of an interferometry system 100. Aspatially extended source 102 directs input light 104 to an interferenceobjective 106 via relay optics 108 and 110 and beam splitter 112. Therelay optics 108 and 110 image input light 104 from spatially extendedsource 102 to an aperture stop 115 and corresponding pupil plane 114 ofthe interference objective 106 (as shown by the dotted marginal rays 116and solid chief rays 117).

In the embodiment of the FIG. 1, interference objective 106 is of theMirau-type, including an objective lens 118, beam splitter 120, andreference surface 122. Beam splitter 120 separates input light 104 intotest light 122, which is directed to a test surface 124 of a test object126, and reference light 128, which reflects from reference surface 122.Objective lens 118 focuses the test and reference light to the test andreference surfaces, respectively. The reference optic 130 supportingreference surface 122 is coated to be reflective only for the focusedreference light, so that the majority of the input light passes throughthe reference optic before being split by beam splitter 120.

After reflecting from the test and reference surfaces, the test andreference light are recombined by beam splitter 120 to form combinedlight 132, which is transmitted by beam splitter 112 and relay lens 136to form an optical interference pattern on an electronic detector 134(for example, a multi-element CCD or CMOS detector). The intensityprofile of the optical interference pattern across the detector ismeasured by different elements of the detector and stored in anelectronic processor (not shown) for analysis. Unlike a conventionalprofiling interferometer in which the test surface is imaged onto thedetector, in the present embodiment, relay lens 136 (e.g., a Bertrandlens) images different points on the pupil plane 114 to correspondingpoints on detector 134 (again as illustrating by dotted marginal rays116 and solid chief rays 117).

Because each source point illuminating pupil plane 114 creates a planewave front for test light 122 illuminating test surface 124, the radiallocation of the source point in pupil plane 114 defines the angle ofincidence of this illumination bundle with respect to the object normal.Thus, all source points located at a given distance from the opticalaxis correspond to a fixed angle of incidence, by which objective lens118 focuses test light 122 to test surface 124. A field stop 138positioned between relay optic 108 and 110 defines the area of testsurface 124 illuminated by test light 122. After reflection from thetest and reference surfaces, combined light 132 forms a secondary imageof the source at pupil plane 114 of the objective lens. Because thecombined light on the pupil plane is then re-imaged by relay lens 136onto detector 134, the different elements of the detector 134 correspondto the different illumination angles of test light 122 on test surface124.

Polarization elements 140, 142, 144, and 146 define the polarizationstate of the test and reference light being directed to the respectivetest and reference surfaces, and that of the combined light beingdirected to the detector. Depending on the embodiment, each polarizationelement can be a polarizer (e.g., a linear polarizer), a retardationplate (e.g., a half or quarter wave plate), or a similar optic thataffects the polarization state of an incident beam. Furthermore, in someembodiments, one or more of the polarization elements can be absent.Moreover, depending on the embodiment, beam splitter 112 can bepolarizing beam splitter or a non-polarizing beam splitter. Details ofvarious embodiments for these polarization elements are describedfurther below. In general, because of the presence of polarizationelements 140, 142 and/or 146, the state of polarization of test light122 at test surface 124 can be a function of the azimuthal position ofthe light in pupil plane 114.

In the presently described embodiment, source 102 provides illuminationover a broad band of wavelengths (e.g., an emission spectrum having afull-width, half-maximum of more than 50 nm, or preferably, even morethan 100 nm). For example, source 102 can be a white light emittingdiode (LED), a filament of a halogen bulb, an arc lamp such as a Xenonarc lamp or a so-called supercontinuum source that uses non-lineareffects in optical materials to generate very broad source spectra (>200nm). The broad band of wavelengths corresponds to a limited coherencelength. As in conventional scanning interferometer, a translation stage150 adjusts the relative optic path length between the test andreference light to produce an optical interference signal at each of thedetector elements. For example, in the embodiment of the FIG. 1,translation stage 150 is a piezoelectric transducer coupled tointerference objective 106 to adjust the distance between the testsurface and the interference objective, and thereby vary the relativeoptical path length between the test and reference light at thedetector.

FIG. 2 shows an exemplary interference signal measured by one of thedetector elements as the translation stage varies the relative opticalpath length between the test and reference light. The interferencesignal is modulated by a contrast envelope corresponding to thecoherence length of the source. The reference surface is positioned inthe interferometer so that a zero optical path length difference betweenthe test and reference light corresponds to a position of the testsurface that is in focus with respect to objective lens 118. Thus,maximum contrast is generally observed when the test surface is in thisin-focus position relative to the interference objective. A measurementis performed by scanning the translation stage over a range larger thanthe coherence length so that the contrast envelope is captured in asequence of intensity patterns measured at the detector.

The interference signal measured at each detector element is analyzed bythe electronic processor, which electronically coupled to both detector134 and translation stage 150. In the presently described embodiment,the electronic processor transforms the interference signal into thefrequency domain, for example, by using a Fourier transform, to extractthe phase and amplitude information for the different wavelengthcomponents of the light source. Preferably, the source spectrum is broadso that many independent spectral components can be calculated with thisprocedure. As will be described in greater detail below, the amplitudeand phase data relate directly to the complex reflectivity of the testsurface, which can be analyzed to determine information about the testobject. Generally, the electronic processor uses information from aseparate calibration to correct the measurement for the reflectivity ofthe reference mirror and other optical characteristics of theinterferometer. Because of the arrangement of interferometry system 100,each detector element of electronic detector 134 provides reflectivitymeasurements at a multiplicity of wavelengths produced by source 102,for a specific angle of incidence and polarization state (according tothe orientations of polarization elements 140, 142, 144 and/or 146). Thecollection of detector elements thus covers a range of angles ofincidence, polarization states and wavelengths, which maximizes theability of the instrument to properly characterize unknown opticalstructures.

A number of calibration procedures can be used to derive the complexreflectivity of the test surface from the measured interference signals.For example, a calibration measurement can be made with a mirror made ofknown bulk material (opaque or transparent) as the test object, and aspectral filter can be used to isolate a selected wavelength from thesource. The interference signals measured on the detector can then beprocessed to determine the angle of incidence corresponding to eachdetector element and the speed of the scanning stage used for dataacquisition. The latter information is useful to properly match theinterference signal spectral components to their respective wavelengths.Additional measurements using objects of known optical properties canalso be used to derive the properties of the interferometer and imagingsystem on a pixel-by-pixel basis. For example, a calibration may includethe steps of calculating the transmission of the system for eachwavelength and at each detector position. Similarly, polarizationeffects such as phase offsets introduced between orthogonal states ofpolarization can also be measured for each detector element and for eachwavelength if required. Specific details for certain embodiments of thecalibration are described further below.

To switch interferometry system 100 from an ellipsometry mode for adetermining the complex reflectivity of the test surface, to a profilingmode for determining, for example, the topography of the test surface,it is sufficient to change the properties of the imaging system so thatthe image of the part comes in focus on the detector instead of theimage of the source. As shown in FIG. 3, this can be accomplished, forexample, by replacing the relay lens 136 by another lens 236 and keepingthe detector position fixed. In this case, the input light from source102 continues to be imaged to pupil plane 114, however, the points on124 are imaged to corresponding points on detector 134 (as indicated bymarginal rays 216 and chief rays 217 from source 102).

Measurement Model

To demonstrate the analysis of the interference signals obtained byinterferometry system 100, we consider an embodiment in whichpolarization elements 140 and 144 are linear polarizers, polarizationelements 142 and 146 are absent, and beam splitter 112 is anon-polarizing beam splitter. The effect of the linear polarizer 140 isto create an identical linear polarization state at every point in pupilplane 114. As a result, the polarization of the light incident on testsurface 124 is linear, but its orientation with respect to the plane ofincidence is a function of the azimuthal location of the source point atthe pupil plane. For example, the source points that belong to a pupildiameter that is parallel to the direction of the linear polarization inthe pupil plane will generate illumination light that is linearlypolarized within the plane of incidence at the test surface (this iscalled the P polarization state). Similarly, the source points thatbelong to a diameter that is perpendicular to the direction of thelinear polarization in the pupil plane will generate illumination lightthat is linearly polarized perpendicularly to the plane of incidence(this is called the S polarization state). Source points that do notbelong to these two diameters will create illumination light on the testsurface that has a mix of S and P polarization states. This is relevantbecause the reflectivity coefficients for the test surface are differentfor S and P polarized light.

The two linear polarizers can have a number of relative orientationsthat will dictate the content of the interference signal detected by thedetector. For example, if the polarizers are parallel then the measuredinterference signal will depend solely on S-polarized test light beingincident on the test surface for one diameter of the pupil plane anddepend solely on P-polarized test light being incident on the testsurface for an orthogonal diameter of the pupil plane (and similarly,for the reference light incident on the reference surface). This isattractive because the difference between the magnitude and phase of Sand P reflectivities is the basis for ellipsometry. If desired,therefore, simplified processing of the data can be restricted to thesetwo diameters. On the other hand, using the data over the entire pupilplane requires taking into account the mix of the two polarizationstates, but provides more data points and thus increases the resolutionof the measurement.

The following analysis applies to the arrangement with the two linearpolarizers aligned parallel to one another. In this case, the amount oftest light that is transmitted through the second linear polarizer(polarization element 144) to detector 134 can be expressed as:$\begin{matrix}{E_{out} = {\frac{1}{2}\left( {{{\cos(\theta)}^{2}{{rp} \cdot {tp}}} - {{\sin(\theta)}^{2}{{rs} \cdot {ts}}}} \right)E_{in}}} & (1)\end{matrix}$where θ is the azimuth angle measured with respect to the direction ofthe polarizers, rp and rs are the complex reflection coefficients of theobject surface for P and S polarization states (known as the “Fresnelreflection coefficients”), tp and ts are the transmission coefficientsfor P and S polarization states for the round trip through theinterference objective 106 and the main beam splitter 112 and E_(out) isthe complex amplitude of the electric field. This model assumes that theoptics are free from birefringence and that reflection off the objectsurface is also free from mechanisms that would mix the S and Ppolarizations states. For example, a uniaxial material with its axisalong the local surface normal can be characterized in this context,however, a material having in-plane birefringence requires a differentmodel.

In practice, the same model applies for the reference light thatpropagates along the reference leg of the interferometer, however, thereflection and transmission coefficients are a priori different:$\begin{matrix}{E_{out}^{r} = {\frac{1}{2}\left( {{{\cos(\theta)}^{2}{{rp}^{r} \cdot {tp}^{r}}} - {{\sin(\theta)}^{2}{{rs}^{r} \cdot {ts}^{r}}}} \right)E_{i\quad n}}} & (2)\end{matrix}$

The interference pattern that is measured at the detector for a givensource wavelength λ and a given source point at the pupil plane consistsof a modulating term that is proportional to the productE_(out)E′_(out):Intensity(k, α, z)=|E _(out)|² +|E′ _(out)|²+2|E _(out) ||E′ _(out)cos(2k cos(α)z+φ(k, α))  (3)where k=2π/λ, λ is the wavelength of the light, z is the verticallocation of the test surface during a mechanical scan relative to a zerooptical path length difference between the test and reference light, αis the angle of incidence of the light at the test surface (whichdepends on the source point location at the pupil) and φ is a phasedifference between the test and reference electric fields. In practice,the signal measured at a given detector location is the sum of all suchsignals generated by the various wavelengths present in the sourcespectrum. As a result, a Fourier transformation of the signal allowsseparating these contributions into complex spectral componentscorresponding to very narrow wavelength ranges. Note that in order toassign a calculated spectral component to a specific source wavelengthone should take into account the correction factor cos(α), which shiftsthe location of these spectral components. This correction factorinvolves knowing the angle of incidence of light at each pixel of thedetector. A calibration of the optical system can be used for this taskand is discussed further below.

FIG. 4 (left side plot) shows a representative interference signalmeasured by a given detector element of detector 134 (corresponding to agiven location in the pupil plane) when measuring a 1003-nm thicksilicon dioxide film on silicon. FIG. 4 (right side plot) shows theresult of Fourier transforming the interference signal to yield thespectral magnitude and phase as function of wavelength (or thecorresponding wavenumber k). The variation in the spectral magnitude andphase is a result of the variation of the Fresnel reflection coefficientas a function of the wavelength (or wavenumber).

In certain embodiments, the frequency transform processing is applied toa region of interest within the image of the pupil plane on thedetector. For example, the region of interest can be an annulus, whichdefines a given range of angles of incidence at the test surface. Theazimuthal location of a pixel (i.e., one of the detector elements)within this annulus defines the mix of S and P polarization thatilluminates the test surface and the radial distance of the pixel to theoptical axis defines the angle of incidence. Furthermore, it can beuseful to extract (possibly using interpolation) the spectral componentsas described above over multiple circles within the region of interest.These components calculated over one such circle can be written in theform: $\begin{matrix}{{Z_{\alpha\quad\lambda\quad\theta} = {L_{\lambda}I_{\alpha\quad\lambda\quad\theta}{\exp\left( {{\mathbb{i}}\quad\varphi_{\alpha\quad\lambda\quad h}} \right)}\left( {{{\cos(\theta)}^{2}\rho_{\alpha\quad\lambda}} - {{\sin(\theta)}^{2}\tau_{\alpha\quad\lambda}}} \right)}}{with}{\rho_{\alpha\quad\lambda} = {{\frac{{rp}_{\alpha\quad\lambda}}{{rs}_{\alpha\quad\lambda}}\quad{and}\quad\tau_{\alpha\quad\lambda}} = \frac{{ts}_{\alpha\quad\lambda}}{{tp}_{\alpha\quad\lambda}}}}} & (4)\end{matrix}$where the subscripts denote a functional dependence, α is the angle ofincidence corresponding to the radius of the circle at the pupil plane,λ is the wavelength of light, θ is the azimuthal angle measured withrespect to the linear polarizers, h is a height offset of the objectsurface, L is a real scaling factor related to the source intensity orsignal strength and I is a complex function that represents thevariations of the light intensity across the source as well as phase andamplitude variations occurring in the optics.

The electronic processor can use the above formula as the key model forthe measurement process. For example, the processor can Fouriertransform the interference signals recorded by the detector to yield thecomponent Z for different wavelengths and angles, of incidence and byinversion extract the complex ratio rp/rs that relates to the testsurface being characterized (e.g., based on Eq. 4). This ratio is calledthe ellipsometric ratio and can also be expressed as: $\begin{matrix}{\rho_{\alpha\quad\lambda} = {\frac{{rp}_{\alpha\quad\lambda}}{{rs}_{\alpha\quad\lambda}} = {{\tan\left( \Psi_{\alpha\quad\lambda} \right)}{\exp\left( {{\mathbb{i}}\quad\Delta_{\alpha\quad\lambda}} \right)}}}} & (5)\end{matrix}$where Ψ and Δ are the two well-known ellipsometric parameters. Standardellipsometry algorithms can then be used to calculate some opticalproperties of the test object, for example, the thickness and refractiveindex of transparent films.

For example, for the case of a homogeneous test surface devoid of films,the electronic processor can readily calculate the complex refractiveindex of the material according to the expression: $\begin{matrix}{{n(\lambda)} = {n_{0}{\tan(\alpha)}\sqrt{1 - {\frac{4\quad\rho_{\alpha\quad\lambda}}{\left( {1 + \rho_{\alpha\quad\lambda}} \right)^{2}}{\sin(\alpha)}^{2}}}}} & (6)\end{matrix}$where n₀ is the refractive index of the ambient medium, usually air. Thetechnique provides in this case the complex refractive index over theentire source spectrum. Data calculated over multiple angles ofincidence can be averaged to improve the measurement resolution.

In another example, for the case of a transparent monolayer having anunknown thickness t and known refractive indices n₀, n₁, n₂ of theambient, film and substrate materials, the electronic processor candetermine the unknown thickness t according to the following equations:$\begin{matrix}{{\alpha_{0} = \alpha}\quad,{\alpha_{1} = {\frac{n_{0}(\lambda)}{n_{1}(\lambda)}{\sin\left( \alpha_{0} \right)}}},{{\alpha_{2} = {\frac{n_{1}(\lambda)}{n_{2}(\lambda)}{\sin\left( \alpha_{1} \right)}}}{{r_{01p} = \frac{\tan\left( {\alpha_{0} - \alpha_{1}} \right)}{\tan\left( {\alpha_{0} + \alpha_{1}} \right)}},{r_{12p} = \frac{\tan\left( {\alpha_{1} - \alpha_{2}} \right)}{\tan\left( {\alpha_{1} + \alpha_{2}} \right)}}}{{r_{01s} = {- \frac{\sin\left( {\alpha_{0} - \alpha_{1}} \right)}{\sin\left( {\alpha_{0} + \alpha_{1}} \right)}}},{r_{12s} = {- \frac{\sin\left( {\alpha_{1} - \alpha_{2}} \right)}{\sin\left( {\alpha_{1} + \alpha_{2}} \right)}}}}{{A = r_{01p}},{B = {r_{12p} + {r_{01p}r_{01s}r_{12s}}}},{C = {r_{12p}r_{01s}r_{12s}}}}{{D = r_{01s}},{E = {r_{12s} + {r_{01p}r_{01s}r_{12p}}}},{F = {r_{01p}r_{12p}r_{12s}}}}{X = \frac{{- \left( {B - {\rho_{\alpha\quad\lambda}E}} \right)} \pm \sqrt{\left( {B - {\rho_{\alpha\quad\lambda}E}} \right)^{2} - {4\left( {C - {\rho_{\alpha\quad\lambda}F}} \right)\left( {A - {\rho_{\alpha\quad\lambda}D}} \right)}}}{2\left( {C - {\rho_{\alpha\quad\lambda}F}} \right)}}{t = {\frac{\mathbb{i}\lambda}{4\quad\pi\quad{n_{1}(\lambda)}{\cos\left( \alpha_{1} \right)}}{\log(X)}}}}} & (7)\end{matrix}$where log is the complex natural logarithm function, i=√{square rootover (−1)} and the sign in the calculation of X is chosen according tothe resulting value of t, which must be real positive. The processing ofthe data obtained by interferometry system 100 provides multipleestimates of t, because the measurement is performed for multiple valuesof α and λ. These multiple estimates can be used to solve for a possibleambiguity in the film thickness associated with the term X in Eq. 7 andto improve the measurement resolution. In other embodiments, theelectronic processor can derive one or more of the refractive indices ofthe test object from the measurement data based on a similar set ofequations.

For more general cases, the electronic processor can use, for example,the “scattering matrix” approach to calculate the reflectioncoefficients of an test surface as a function of its unknown parameters(refractive indices, film thicknesses, layer roughness, refractive indexgradients, etc). The reflection coefficient functions are applied tocalculate the ellipsometric parameters Ψ^(model) and Δ^(model) for guessvalues of the unknown parameters. An iterative algorithm is then used tovary these parameters in order to minimize the sum of the squareddifferences between the measured ellipsometric coefficients andcorresponding model coefficients:χ²Σ(Ψ_(αλ)−Ψ_(αλ) ^(mod el))²+Σ(Δ_(αλ)−Δ_(αλ) ^(mod el))  (8)Alternative merit functions can be defined that include for exampleweighting factors for the different wavelengths and angles of incidence.Such approaches are described, for example, in R. M. A. Azzam and N. M.Bashara, “Ellipsometry and Polarized Light,” Elsevier Science B. V.,ISBN 0 444 87016 4 (paperbook), 1987.

System Calibration

In certain embodiments, a first step of the system calibration includescalculating the angle of incidence of a beam bundle at the test surfacebased on the location of the source point in the pupil plane. In otherwords, we want to assign an angle of incidence a to each pixel in thedetector corresponding to the image of the pupil plane. This can beaccomplished, for example, by performing a measurement with a narrowbandfilter so that the light detected by the detector is essentiallymonochromatic and has a known wavelength. In this case, Equation (3)shows that the frequency of the interference signal is proportional tothe source wavelength and the angle of incidence through therelationship k cos α. The signal frequency can be calculated by aFourier transform of the signal and the angle of incidence can bederived from the knowledge of the scan rate of the translation stage andthe source wavelength.

Furthermore, to the extent the scan rate of the translation stage isinitially unknown, it can be determined by locating the pixel on thedetector whose interference signal has the largest frequency. Accordingto the frequency's dependence on the relationship k cos α, this pixelcorresponds to normal incidence (i.e., α=0), and so the stage speed canbe extracted directly from the measured frequency and knowledge of thesource wavelength.

Note that a priori information on the way the microscope objective mapsangles in object space onto pupil positions can also be used to improvethe quality of this calibration. For example, a typical objective iscorrected for coma (a geometric aberration), which implies that the raymapping at the pupil should nominally obey the so-called “Abbé sinecondition.” This condition means that the radial distance of a sourcepoint from the optical axis at the pupil is directly proportional to thesine of the angle of incidence in object space. One can thus calculatethe angle of incidence for each pixel and then fit a global functionderived from the sine condition to provide an analytical functionmapping pupil position to angle of incidence.

In certain embodiments, the procedure outlined above can be repeated fordifferent nominal source wavelengths so that chromatic variations of theangular mapping are taken into account. A by-product of the fittingprocedure is the pixel position of the optical axis at the pupil. Thatinformation is also recorded as a function of wavelength and can be usedlater on to apply corrections to angle of incidence calculations.

For certain embodiments, the second stage of the calibration involvescalculating the value of the various system parameters that relate theobservable Z expressed in in Eq. (4) to the ellipsometric ratio.

For example, this can accomplished by measuring two samples that haveknown optical properties, for example calibration wafers typically usedwith ellipsometers. For each angle of incidence and wavelength ofinterest the electronic processor determines the spectral components Zas a function of azimuth angle θ as in Eq. (4) for both samples. Theratio of these components is then calculated, yielding the complex ratioz as a function of θ: $\begin{matrix}{{z_{\alpha\quad\lambda\quad\theta} = {\frac{Z_{\alpha\quad\lambda\quad\theta}^{a}}{Z_{\alpha\quad\lambda\quad\theta}^{b}} = {\frac{L_{\lambda}^{a}}{L_{\lambda}^{b}}{\exp\left( {{{\mathbb{i}}\quad\varphi_{\alpha\quad\lambda\quad{ha}}} - {{\mathbb{i}}\quad\varphi_{\alpha\quad\lambda\quad{hb}}}} \right)}\frac{{{\cos(\theta)}^{2}\rho_{\alpha\quad\lambda}^{a}} - {{\sin(\theta)}^{2}\tau_{\alpha\quad\lambda}}}{{{\cos(\theta)}^{2}\rho_{\alpha\quad\lambda}^{b}} - {{\sin(\theta)}^{2}\tau_{\alpha\quad\lambda}}}}}}{or}{z_{\alpha\quad\lambda\quad\theta} = {{zs}_{\alpha\quad\lambda}\frac{{{\cos(\theta)}^{2}\rho_{\alpha\quad\lambda}^{a}} - {{\sin(\theta)}^{2}\tau_{\alpha\quad\lambda}}}{{{\cos(\theta)}^{2}\rho_{\alpha\quad\lambda}^{b}} - {{\sin(\theta)}^{2}\tau_{\alpha\quad\lambda}}}}}} & (9)\end{matrix}$where zs_(αλ) and τ_(αλ) are unknown complex numbers and the a or bsuperscripts identify one or the other calibration sample. ρ_(αλ) ^(a)and ρ_(αλ) ^(b) are calculated using the ratio of the reflectioncoefficients for the two materials. These coefficients are themselvescalculated using the known material properties and known filmthicknesses (if present) of the calibration samples. The electronicprocessor can then use a solver, for example a least-squares solverbased on the Levenberg-Marquardt algorithm, to find the value of the twounknown parameters that minimize the difference between the quantitiescalculated on both sides of Equation (9). The process is repeated forother angles of incidence and wavelengths.

In a further step, if desired, the maps zs_(αλ) and τ_(αλ) are filteredand/or fitted to analytical functions. It is then possible to reprocessthe spectral components obtained for each sample and derive anothercalibration parameter, the function J: $\begin{matrix}{{J_{\alpha\quad\lambda\quad\theta} = {\frac{Z_{\alpha\quad\lambda\quad\theta}^{a}}{{{\cos(\theta)}^{2}\rho_{\alpha\quad\lambda}^{a}} - {{\sin(\theta)}^{2}\tau_{\alpha\quad\lambda}}} = {L_{\lambda}^{a}I_{\alpha\quad\lambda\quad\theta}{\exp\left( {{\mathbb{i}}\quad\varphi_{\alpha\quad\lambda\quad{ha}}} \right)}}}}{or}{J_{\alpha\quad\lambda\quad\theta} = {{\frac{Z_{\alpha\quad\lambda\quad\theta}^{b}}{{{{cso}(\theta)}^{2}\rho_{\alpha\quad\lambda}^{b}} - {{\sin(\theta)}^{2}\tau_{\alpha\quad\lambda}}}{zs}_{\alpha\quad\lambda}} = {L_{\lambda}^{a}I_{\alpha\quad\lambda\quad\theta}{\exp\left( {{\mathbb{i}}\quad\varphi_{\alpha\quad\lambda\quad{ha}}} \right)}}}}} & (10)\end{matrix}$

In practice, the two expressions for J shown in Equation (10) can beaveraged. The calculated values of J as a function of angle ofincidence, wavelength and azimuth angle are then stored by theelectronic processor in a calibration file along with the definition ofthe function τ_(αλ).

Note that the procedure outlined above could be extended to more thantwo samples in order to benefit from redundancy in the calculation.

In certain embodiments, another step of the calculation involvesestablishing the exact angular orientation of the polarizers withrespect to the coordinate system of the pupil as seen by the detector.This can be done, for example, by observing that Equation (9) isperiodic in θ with a period π. It follows that the phase of the evencomponents of the Fourier transform of the ratio z is a directmeasurement of the angular offset of the polarizer. Accordingly, thiscalculation can be performed before determining zs_(αλ) and τ_(αλ).

Characterization of an Unknown Test Object

In certain embodiments, by using the stored calibration information, theelectronic processor can characterize an unknown test object as follows.The interference data recorded for an unknown object surface areprocessed as for the calibration and yield rings of data according toEquation (4), where the superscript c denotes the unknown test object:Z _(αλθ) ^(c) L _(λ) ^(c) I _(αλθ)exp(iφ _(αλhc))(cos(θ)²ρ_(αλ)^(c)−sin(θ)²τ_(αλ))  (11)

Each ring is processed using the calibration information. First, thefunction J is retrieved for the specific angle of incidence andwavelength and a new complex ratio is calculated: $\begin{matrix}{{z_{\alpha\quad\lambda\quad\theta} = {\frac{Z_{\alpha\quad\lambda\quad\theta}^{c}}{J_{\alpha\quad\lambda\quad\theta}} = {\frac{L_{\lambda}^{c}}{L_{\lambda}^{a}}{\exp\left( {{{\mathbb{i}}\quad\varphi_{\alpha\quad\lambda\quad{hc}}} - {{\mathbb{i}}\quad\varphi_{\alpha\quad\lambda\quad{ha}}}} \right)}\left( {{{\cos(\theta)}^{2}\rho_{\alpha\quad\lambda}^{c}} - {{\sin(\theta)}^{2}\tau_{\alpha\quad\lambda}}} \right)}}}{or}{z_{\alpha\quad\lambda\quad\theta} = {\frac{Z_{\alpha\quad\lambda\quad\theta}^{c}}{J_{\alpha\quad\lambda\quad\theta}} = {\eta_{\alpha\quad\lambda}\left( {{{\cos(\theta)}^{2}\rho_{\alpha\quad\lambda}^{c}} - {{\sin(\theta)}^{2}\tau_{\alpha\quad\lambda}}} \right)}}}} & (12)\end{matrix}$where η_(αλ) and ρ_(αλ) ^(c) are unknown complex parameters independentof the azimuth angle θ. A numerical solver is applied again to find thevalue of these parameters that provide the best match between themeasured ratio z and the model on the right hand side of Equation (12).An important result of the calculation is the parameter ρ_(αλ) ^(c),which is the ellipsometric ratio for the unknown object surface.

As described above with reference, for example, to Eqs. 6-8, theelectronic processor can process the ellipsometric ratio according to amodel of the test object to extract information about the test object,such as the refractive index and/or thickness of one or more layers.

The graphs in FIG. 5 show experimental data derived using the aboveanalysis for a 675-nm thick SiO₂ monolayer on a silicon substrate. Thegraphs show the real and imaginary parts of Z_(αλθ) ^(c) (left sideplot) and z_(αλθ) (right side plot) measured experimentally for α=43°and λ=576 nm. As shown, the derived ratio z_(αλθ) exhibits the7-periodicity expected from the model in Equation (12).

Note that in order to create the ring of data defined in Equation (11),the location of the optical axis at the detector should be known. Thislocation may have changed since the calibration. For example, becausethe instrument may have been switched from the surface characterizationmode to the topography mode, one cannot assume that the projection ofthe center of the pupil at the detector remains constant. Hence, incertain embodiments, a preliminary step of the process can involvecalculating the frequency spectrum at each detector element, deriving anominal mean frequency for each pixel (e.g., the mean frequency can becalculated as the centroid of the measured spectrum), and analyzing themap of mean frequency to find the location of the pupil center. Asmentioned in the calibration section above, the mean frequency for agiven source spectrum is expected to scale with the cosine of the angleof incidence in object space. Hence, the pupil location where the meanfrequency is maximum corresponds to the optical axis. In someembodiments, this location can be calculated by fitting an evenfunction—such as a parabola—to the map of mean frequencies and definingthe apex of the parabola as the location of the optical axis.Alternatively, a preliminary measurement can be performed with anarrowband filter inserted in the system, as in the system calibration.

For simplicity and ease of expression, the procedures outlined in theabove sections are based on certain assumptions about the nature of thetest surface and the optical system. However, more advanced models canbe used for more complicated cases to extract information about the testobject from the interference signals measured by system 100. Forexample, a different model can be used when the test structure mayexhibit birefringence, while the calibration procedure based onnon-birefringent calibration samples remains the same.

Additional Configurations of the Polarization Elements

The analytical sections above were based on an embodiment in whichpolarization elements 140 and 144 are linear polarizers orientedparallel to one another, polarization elements 142 and 146 are absent,and beam splitter 112 is non-polarizing. In another embodiment, ananalytically equivalent configuration that guarantees the parallelism ofthe linear polarizers involves removing polarization elements 140 and144, and having polarization element 142 being a linear polarizer,because it is positioned in the path of both the input light beingdirected to the interference objective and the combined light beingdirected to the detector. In another embodiment, polarization elements140 and 144 can be linear polarizers that oriented orthogonal to oneanother, in which case the amount of light coming back from the objectis a periodic function of the azimuthal position multiplied by anazimuth-independent weighted sum of the S and P reflectivity. Suchinformation can also be processed to determine information about thetest object.

In yet another embodiment, polarizing elements 140, 144 and 146 areabsent, whereas the beam splitter 112 is of the polarizing type andpolarization element 142 is a quarter wave plate. Proper alignment ofthe quarter wave plate with its fast and slow axes at 45° from thepolarization axis defined by beam splitter 112 results in a circularpolarization state at every point of the pupil. The contribution of Sand P polarizations in the detected interference signal is then tofirst-order independent of the azimuthal position of the source points.It is thus possible to combine the information collected over groups ofdetector elements that reside at fixed distances from the optical axisto improve the signal to noise ratio of the overall measurement. Notethat depending on the nature of the quarter wave plate more advancedprocessing may be required to account for example for the variation ofretardance with wavelength, which introduces a small azimuthaldependence on the polarization state of the source points at the pupil.This can be modeled mathematically using, for example, Jones matricesand vectors, as is known in the art.

In yet another embodiment, polarization element 140 is absent, beamsplitter 112 is of the polarizing type, polarization element 142 is aquarter wave plate, polarization element 144 is absent, and polarizationelement 146 is a linear polarizer attached to interference objective106. Because of the linear polarizer, this embodiment is analyticallyequivalent to the first embodiment with parallel linear polarizers.However, the addition of a polarizing beam splitter and quarterwaveplate improves the light efficiency of the system when a differentmicroscope objective (without polarizer attached) is mounted to thesystem, for use, for example, in the profiling mode of operation. Asdescribed in greater detail below, switching back and forth betweendifferent microscope objectives can be accomplished with an objectiveturret, which can be motorized under the control of the electronicprocessor for a production line instrument.

Reflectometry Mode

In yet another embodiment, polarization elements 140, 142, 144 and 146are all absent and the beam splitter is of the non polarizing type. Fora typical broadband source such as the filament in a halogen bulb or theemissive material of a white-light LED, the illumination input light isunpolarized, which means that for every source point at the pupil thepolarization state can be described as an equal mix of S and Ppolarization components. In this case the measured signal is expected tobe again independent from the azimuthal source position to the firstorder. In this case the system is capable of measuring the amount oflight reflected by the object for different angles of incidence, as in areflectometer. However, contrary to a conventional reflectometer thatcaptures light one wavelength at a time, interferometry system 100 cancapture all source wavelengths in the course of a single measurement.These spectral components are separated using the analysis of the signalin the frequency domain described above. While this reflectometry modeof operation does not provide as much information about the test surfacereflectivity as the ellipsometry modes described above, thereflectometry information is still sensitive to variations in theproperties of the test object. For example, the reflectometry data canbe compared to models of the test object to determine the materialcomposition at a given location in a heterogeneous sample, refractiveindices, thicknesses, and/or the presence or absence of defects.

Selective Signal Analysis for Thin Film Samples

When the test object includes one or more films, the multiple interfacesproduce multiple reflections that contribute the interference signalmeasured at each detector element. For the case of a broadband lightsource, the interference signal measured at various locations at inpupil plane have a limited coherence length, as shown by the signalenvelope in FIG. 2 and FIG. 4 (left side). When the film is sufficientlythick that the round-trip optical thickness is larger than the coherencelength, the measured signal consists of multiple separable signals, eachsignal corresponding to an interface between two materials.

An example of such a signal is shown in FIG. 6 for a 5-μm thick silicondioxide (SiO₂) film on silicon (Si). In this case, the weaker signal tothe right corresponds to the air/SiO₂ interface. The larger signal inthe center corresponds to the SiO₂/Si interface. The weak signal on theleft is due to a double pass reflection of light in the SiO₂ layer. Inthis case, it is possible to process each portion of the signalcorresponding to a given interface independently to simplify the samplemodel (e.g., limit the number of unknown parameters) and therebysimplify or improve the robustness of the analysis.

For example, in certain embodiments, the electronic processor mayprocess the portion of the signal corresponding to the air/top layerinterface so that the analysis becomes equivalent to measuring aninfinitely thick slab of the top layer material. In this case therefractive index of the material can be readily calculated usingEquation (6) and there is no need to include in the modeling the effectof underlying layers and possibly complex structures such as those foundon patterned semiconductor wafers.

Furthermore, in certain embodiments, after the electronic processoranalyzes the portion of the signal corresponding to the top interface,the processing can be repeated for the entire signal (or other portionsof the signal) by including the signal portions corresponding to theunderlying interface. The model required to process the ellipsometrydata is more complicated in this case, however, because the initialprocessing yields the refractive index of the top layer, the processingis simpler than it would have been in the absence of the initialprocessing. For example, the refractive index of a thick monolayer canbe first calculated using Equation (6) when processing the rightmostsignal. Assuming the substrate material is known, the processing of theentire interference signal (including the entire trace shown in FIG. 6,for example) yields new ellipsometric parameters that provide the filmthickness using Equation (7). The benefit is the ability to separate thecalculation of the refractive index and physical thickness.

For the case of a multilayer stack made of sufficiently thick layers,one can apply a bootstrap procedure that starts with the first signalyielding the refractive index of the first layer. The processing of thefirst and second signals simultaneously then yields the thickness of thefirst layer and the refractive index of the second layer. The processingof the first, second and third signals then yields the thickness of thesecond layer and the refractive index of the third layer, and so on. Thebenefit again is that one does not need to use an ellipsometric modelthat includes all interfaces at once with all materials and thicknessesbeing unknowns, as is common in conventional ellipsometers.

Even for small film thicknesses that cause the interference signalassociated with each interface to partially overlap, it may still bepossible to isolate a portion of the interference signal correspondingto a given interface and separately process that portion. See, forexample, U.S. patent application Ser. No. 10/941,649 entitled “METHODSAND SYSTEMS FOR INTERFEROMETRIC ANALYSIS OF SURFACES AND RELATEDAPPLICATIONS” and published as U.S. Patent Publication No.US-2005-0078318-A1, the contents of which are incorporated herein, whichdescribes such techniques in the context of a profiling mode.

Profiling Mode Analysis

As described above, interferometry system 100 can switch from anellipsometry (or reflectometry) mode for a determining reflectivityinformation about the test surface, to a profiling mode for determining,for example, the topography of the test surface. As shown in FIG. 3,this can be accomplished, for example, by replacing the relay lens 136by another lens 236 that images test surface to the detector (ratherthan image the pupil plane to the detector). This configurationcorresponds to a conventional scanning interferometer for surfaceprofiling. In what follows, a mathematical formalism for the surfaceprofiling operation is described.

For a bulk material test object (i.e., no thin film structure), theinterference phase φ to first order in the angular wavenumber k=2π/λwith respect to a reference datum plane in the test leg can be expressedas:φ(k)=2nk (h−ζ)+(γ_(part)+γ_(sys))+(τ_(part)+τ_(sys))(k−k ₀),  (13)where k₀ is the nominal wavenumber, ζ is the scan coordinate for thetranslation stage, γ_(part) is the part surface phase change onreflection (PCOR), and γ_(sys) is the system phase offset attributableto the interferometer system. The value γ_(sys) includes PCORcontributions from the interferometer optics and any constant offsetsresulting, e.g., from the starting position of the scan ζ. The lineardispersions coefficients τ_(part) and τ_(sys) correspond to the phaseoffsets γ_(part) and γ_(sys), respectively. The phase offsets γ_(part),γ_(sys) are evaluated at the nominal wavenumber k₀. The index ofrefraction n for air and is assumed to be independent of wavenumber.Those skilled in the art will appreciate that the teachings of theinvention can be extended to denser transparent media than air by takinginto account the wavenumber dependence of material index. All of theterms in Eq. 13 are potentially a function of field position x,y,although for the subsequent description, the variables n, ζ, k₀ areassumed to be constant over the field of view.

Because of the broad band radiation from the light source, interferencefringes are only produced when the optical path difference (OPD) betweenthe reference and measurement legs are within the coherence length ofthe broadband radiation. Thus, scanning interferometric measurements canbe considered a “coherence profiling” mode in that it uses the broadbandnature of the interference effect, e.g., the localization of fringecontrast or equivalently, the measurement of the rate of change ofinterference phase with wavenumber. As a result, the interference signalI measured by each detector element can be expressed as:I=1+V[h+(τ_(sys)+τ_(part))/2n−ζ]cos[2nk ₀(h−ζ)+γ_(part)+γ_(sys)]  (14)where V is the fringe contrast envelope. The envelope V is proportionalto the Fourier Transform of the spectral distribution of the light fromthe light source.

For a symmetric contrast envelope, the peak value of the fringe contrastenvelope is given by the scan position for which dφ/dk=0. This is thestationary phase position, where the interference phase is the sameindependent of wave number, and all of the interference patterns add upconstructively. More generally, it can be shown that the stationaryphase condition dφ/dk=0 corresponds to the centroid of the fringecontrast envelope V. The phase gap G between the stationary phaseposition and the nearest zero phase point φ=0 position is given byG=(γ_(part)+γ_(sys))−k ₀ (τ_(sys)+τ_(part)).  (15)This is a constant phase offset, independent of wavenumber k, butdependent on the system and part parameters. The phase φ₀ is the phaseat the nominal wavenumber k₀ (with respect to a ζ=0 scan position),e.g., from Eq. (13) we haveφ₀=2nk ₀ h+(γ _(part)+γ_(sys)).  (16)

From Eq. 14 it can be seen that the maximum or peak fringe contrastoccurs at the scan position ζ=h+(τ_(sys)+τ_(part))/2n. Thus, in one dataprocessing embodiment, the electronic processor, when operating in theprofiling mode, determines the fringe-contrast envelope V as a functionof ζ, e.g., by electronic or digital conversion, for every detectorpixel. It then determines the scan position ζ_(max) for which theenvelope V reaches a specific value, e.g., its maximum or peak value.The corresponding height h for each location on the test object is thisscan position minus the dispersion offset:h=ζ _(max)−(τ_(sys)−τ_(part))/2n.  (17)

In another signal processing method, the coherence profiling intensitysignal is Fourier transformed with respect to the scan position ζ intothe frequency domain (i.e., with respect to frequency wave number k).The phase of the transformed data corresponds directly to the phase φ(k)in Eq. 13. From this phase, the signal processor calculates the phasederivative dφ/dk, and determines height h for each detector pixelaccording to: $\begin{matrix}{h = {{\frac{1}{2n}\frac{\mathbb{d}\phi}{\mathbb{d}k}} - {{\left( {\tau_{sys} - \tau_{part}} \right)/2}n}}} & (18)\end{matrix}$where the derivative dφ/dk is calculated for ζ=0. Eq. 18 followsdirectly from Eq. 13.

From Eqs. 17 and 18, one sees that surface height measurements based oncoherence profiling data can be more accurately calculated byaccounting, e.g., by calibration, for PCOR dispersion for theinterferometry system and the test part (e.g., τ_(part) and τ_(sys)). Tothe extent the PCOR factors are constant across the field of view, notaccounting for them will only introduce overall shift in the surfaceprofile and the resulting surface topography is accurate. However, whenthe PCOR factors change because of, for example, variations in thesurface material, they should be accounted for to provide a moreaccurate surface topography profile.

In addition to coherence profiling, surface height measurements can alsobe based on interferometric phase profiling data where theinterferometric phase φ(k) is measured directly for one or morewavenumbers k. For example, phase shifting interferometry (PSI)techniques can be used for such measurements. From Eq. 13, it is clearthat if direct interferometric phase measurements are used to determineheight h, accounting for PCOR γ_(part) and γ_(sys) (and PCOR dispersionτ_(part) and τ_(sys) for wave numbers other than the nominal wave numberk₀) improves the accuracy of the height measurement.

Generally, the sensitivities to particular noise sources for coherenceprofiling measurements differ from those for phase profilingmeasurements, thus a particular technique may be preferable for aparticular application, or they may be used to complement one another.One drawback of many phase profiling measurements, however, is themeasured phase φ(k) includes 2π fringe ambiguity. For relatively smoothsurfaces, relative fringe ambiguity over the surface may be interpolatedfrom the data of multiple detector pixels using standard fringeunwrapping procedures. More generally, however, it is preferable to havean independent measurement, such as coherence profiling data, to removesuch fringe ambiguity. Thus, to obtain absolute surface profilemeasurements, the coherence profiling height measurement can be usedalone, or it can be used to remove the absolute fringe ambiguity fromthe phase profiling measurement, which may be more accurate than thecoherence measurement in some cases.

In one such embodiment, the height h determined from a coherenceprofiling measurement is used to calculate an absolute phase profilingheight measurement h′ based on phase profiling data for the phaseφ₀=φ(k₀) according to: $\begin{matrix}{h^{\prime} = {\frac{1}{2{nk}_{0}}\left\{ {\left( {\phi_{0} - \gamma_{part} - \gamma_{sys}} \right) - {2\pi\quad{{Int}\left\lbrack \frac{\left( {\phi_{0} - \gamma_{part} - \gamma_{sys}} \right) - \left( {2k_{0}{nh}} \right)}{2\pi} \right\rbrack}}} \right\}}} & (19)\end{matrix}$where Int [ ] returns the nearest integer to its argument. Eq. 19 can beapplied independently to every point x,y on the part surface. Again, asis apparent from Eq. 19, accounting for PCOR γ_(part) and γ_(sys)improves the accuracy of the absolute phase profiling measurement.Moreover, Eq. 19 implicitly depends on PCOR dispersion values τ_(part)and τ_(sys) through the coherence profiling determination of h.

For more complex samples, such as those with thin films, the profilingformalism is more complicated because reflections from underlyingsurfaces will also contributed the interference signal. Where thelimited coherence length of input light is small enough relative to filmthickness to separate the interferometry signal into portionscorresponding to each interface, the electronic processor can isolatethat portion of the interferometry signal corresponding to the interfaceof interest and process it using the general formalism described aboveto extract the surface topography for that interface. Furthermore, evenfor small film thicknesses that cause the interference signal associatedwith each interface to partially overlap, it may still be possible toisolate a portion of the interference signal corresponding to a giveninterface and separately process that portion. See, for example, U.S.patent application Ser. No. 10/941,649 entitled “METHODS AND SYSTEMS FORINTERFEROMETRIC ANALYSIS OF SURFACES AND RELATED APPLICATIONS” andpublished as U.S. Patent Publication No. US-2005-0078318-A1, which wasincorporated by reference above. In yet further embodiments, theelectronic processor can use the model-based techniques disclosed inU.S. patent application Ser. No. 10/795,579 entitled “PROFILING COMPLEXSURFACE STRUCTURES USING SCANNING INTERFEROMETRY” and published as U.S.Patent Publication No. US-2004-0189999-A1, the contents of which isincorporated herein by reference, to determine profile information forcomplex surface structures.

Additional Embodiments for Profiling

Instead of switching out relay lens 136, in further embodiments, forexample, the relay lens can be left alone and detector 134 can betranslated to a position where the test surface is in focus. This isshown schematically in FIG. 7, which shows detector 134 coupled to amotorized translation stage 760 under the control of electronicprocessor 770 to adjust the detector position for receiving combinedlight 132 relative to the rest of the interferometry system 700. Thetranslation stage allows the system to switch between a first positioncorresponding the ellipsometry mode, in which the pupil plane is imagedto the detector, and a second position corresponding to the profilingmode, in which the test surface is imaged to the detector.

In yet a further embodiment, shown schematically in FIG. 8, a beamsplitter 810 can split the combined light 132 received from the rest ofthe interferometry system 800 into two channels with two correspondingmulti-element detectors 880 and 890, with one channel using relay optics875 to image pupil plane 114 to the first detector 880 to provide theellipsometry mode measurement and the other channel using relay optics885 to image the test surface to the second detector 890 tosimultaneously provide the profiling mode measurement. Both detectorsare coupled to electronic processor 870, which analyze the detectorimages as described above.

Various combinations of these approaches are also possible. For example,the system can include optics that image the pupil plane to a firstportion of a common electronic detector and image the test surface to asecond portion of the common electronic detector. In this case, thedifferent portions of the common electronic detector can be consideredto be separate detectors.

Multi-Mode Operation and Applications

FIG. 9 shows a schematic diagram of how various components ininterferometry system 100 can be automated under the control ofelectronic processor 970, which, in the presently described embodiment,can include an analytical processor 972 for carrying out mathematicalanalyses, device controllers 974 for controlling various components inthe interferometry system, a user interface 976 (e.g., a keyboard anddisplay), and a storage medium 978 for storing calibration information,data files, a sample models, and/or automated protocals.

First, the system can include a motorized turret 910 supporting multipleobjectives 912 and configured to introduce a selected objective into thepath of input light 104. One or more of the objectives can beinterference objectives, with the different interference objectivesproviding different magnifications. Furthermore, in certain embodiments,one (or more) of the interference objectives can be especiallyconfigured for the ellipsometry mode of operation by having polarizationelement 146 (e.g., a linear polarizer) attached to it. The remaininginterference objectives can be used in the profiling mode and, incertain embodiments, can omit polarization element 146 so as to increaselight efficiency (such as for the embodiment described above in whichbeam splitter 112 is a polarizing beam splitter and polarization elementis 142 is a quarter wave plate). Moreover, one or more of the objectivescan be a non-interferometric objective (i.e., one without a referenceleg), each with a different magnification, so that system 100 can alsooperate in a conventional microscope mode for collecting optical imagesof the test surface (in which case the relay lens is set to image oftest surface to the detector). Turret 910 is under the control ofelectronic processor 970, which selects the desired objective accordingto user input or some automated protocol.

Next, the system includes a motorized stage 920 (e.g., a tube lensholder) for supporting relay lenses 136 and 236 and selectivelypositioning one of them in the path of combined light 132 for selectingbetween the first mode (e.g., an ellipsometry or reflectometry mode) inwhich the pupil plane 114 is imaged to the detector and the second mode(e.g., profiling or microscope mode) in which the test surface is imagedto the detector.

Motorized stage 920 is under the control of electronic processor 970,which selects the desired relay lens according to user input or someautomated protocol. In other embodiments, in which a translation stageis moved to adjust the position of the detector to switch between thefirst and second modes, the translation is under control of electronicprocessor. Furthermore, in those embodiments with two detectionchannels, each detector is coupled to the electronic processor 970 foranalysis.

Furthermore, the system can include motorized apertures 930 and 932under control of electronic processor 970 to control the dimensions offield stop 138 and aperture stop 115, respectively. Again the motorizedapertures are under the control of electronic processor 970, whichselects the desired settings according to user input or some automatedprotocol.

Also, translation stage 150, which is used to vary the relative opticalpath length between the test and reference legs of the interferometer,is under the control electronic processor 970. As described above, thetranslation stage can be coupled to adjust the position of theinterference objective relative to a mount 940 for supporting testobject 126.

Alternatively, in further embodiments, the translation stage can adjustthe position of the interferometry system as a whole relative to themount, or the translation stage can be coupled to the mount, so it isthe mount that moves to vary the optical path length difference.

Furthermore, a lateral translation stage 950, also under the control ofelectronic processor 970, can be coupled to the mount 940 supporting thetest object to translate laterally the region of the test surface underoptical inspection. In certain embodiments, translation stage 950 canalso orient mount 940 (e.g., provide tip and tilt) so as to align thetest surface normal to the optical axis of the interference objective.

Finally, an object handling station 960, also under control ofelectronic processor 970, can be coupled to mount 940 to provideautomated introduction and removal of test samples into system 100 formeasurement. For example, automated wafer handling systems known in theart can be used for this purpose. Furthermore, if necessary, system 100and object handling system can be housed under vacuum or clean roomconditions to minimize contamination of the test objects.

The resulting system provides great flexibility for providing variousmeasurement modalities and procedures. For example, the system can firstbe configured in the microscope mode with one or more selectedmagnifications to obtain optical images of the test object for variouslateral positions of the object. Such images can be analyzed by a useror by electronic processor 970 (using machine vision techniques) toidentify certain regions (e.g., specific structures or features,landmarks, fiducial markers, defects, etc.) in the object. Based on suchidentification, selected regions of the sample can then be studied inthe ellipsometry mode to determine sample properties (e.g., refractiveindex, underlying film thickness(es), material identification, etc.).

Accordingly, the electronic processor causes stage 920 to switch therelay lens to the one configured for the ellipsometry mode and furthercauses turret 910 to introduce a suitable interference objective intothe path of the input light. To improve the accuracy of the ellipsometrymeasurement, the electronic processor can reduce the size of the fieldstop via motorized aperture 930 to isolate a small laterally homogenousregion of the object. After the ellipsometry characterization iscomplete, electronic processor 970 can switch the instrument to theprofiling mode, selecting an interference objective with a suitablemagnification and adjusting the size of field stop accordingly. Asdescribed above, the profiling mode captures interference signals thatallow reconstructing the topography of, for example, one or moreinterfaces that constitute the object. Notably, as described in greaterdetail below, the knowledge of the optical characteristics of thevarious materials determined in the ellipsometry mode allows forcorrecting the calculated topography for thin film or dissimilarmaterial effects that would otherwise distort the profile. See, forexample, U.S. patent application Ser. No. 10/795,579 entitled “PROFILINGCOMPLEX SURFACE STRUCTURES USING SCANNING INTERFEROMETRY” and publishedas U.S. Patent Publication No. US-2004-0189999-A1, which wasincorporated by reference above. If desired, the electronic processorcan also adjust the aperture stop diameter via motorized aperture 932 toimprove the measurement in any of the various modes.

When used in conjunction with automated object handling system 960, themeasurement procedure can be repeated automatically for a series ofsamples. This could be useful for various process control schemes, suchas for monitoring, testing, and/or optimizing one or more semiconductorprocessing steps.

For example, the system can be used in a semiconductor process for toolspecific monitoring or for controlling the process flow itself. In theprocess monitoring application, single/mulit-layer films are grown,deposited, polished, or etched away on unpatterned Si wafers (monitorwafers) by the corresponding process tool and subsequently the thicknessand/or optical properties are measured using the interferometry systemdisclosed herein (for example, by using the ellipsometry mode, theprofiling mode, or both). The average, as well as within waferuniformity, of thickness (and/or optical properties) of these monitorwafers are used to determine whether the associated process tool isoperating with targeted specification or should be retargeted, adjusted,or taken out of production use.

In the process control application, latter single/mulit-layer films aregrown, deposited, polished, or etched away on patterned Si, productionwafers by the corresponding process tool and subsequently the thicknessand/or optical properties are measured with the interferometry systemdisclosed herein (for example, by using the ellipsometry mode, theprofiling mode, or both). Production measurements used for processcontrol typical include a small measurement site and the ability toalign the measurement tool to the sample region of interest. This sitemay consists of multi-layer film stack (that may itself be patterned)and thus requires complex mathematical modeling in order to extract therelevant physical parameters. Process control measurements determine thestability of the integrated process flow and determine whether theintegrated processing should continue, be retargeted, redirected toother equipment, or shut down entirely.

Specifically, for example, the interferometry system disclosed hereincan be used to monitor the following equipment: diffusion, rapid thermalanneal, chemical vapor deposition tools (both low pressure and highpressure), dielectric etch, chemical mechanical polishers, plasmadeposition, plasma etch, lithography track, and lithography exposuretools. Additionally, the interferometry system disclosed herein can beused to control the following processes: trench and isolation,transistor formation, as well as interlayer dielectric formation (suchas dual damascene).

Combining Information from Different Modes

One powerful feature of interferometry system 100 is that not only is itpossible to gather rapidly and in automated fashion information aboutthe test object for a variety of measurement modes, but also, thatinformation determined from one mode of operation can be used to improvethe accuracy of the measurement in the other mode of operation.

For example, when in the ellipsometry mode of operation, the electronicprocessor can determine the optical properties of various materialspresent at different locations on an object (for example copper linesseparated by dielectric regions on a semiconductor wafer). In suchcases, each material typically requires a separate measurement. Oncethese properties are known it is possible to calculate the phase changeon reflection (PCOR) undergone by light reflecting off the objectsurface. As described above in the profiling analysis section, thesephase changes are material dependent and affect the topographymeasurement. For example, copper regions appear lower than they trulyare with respect to the dielectric regions. However, the knowledge ofthe material dependent phase changes determined in the ellipsometry modeallows the electronic processor to correct the topography map to obtainthe true surface topography. In practice, the phase change on reflectionfor a given angle of incidence and wavelength affects the measuredsignal as a contribution to the parameter φ in Equation 20. For example,one can write:φ_(αλ)φ_(αλ) ^(system)−φ_(αλ) ^(part)  (20)where φ_(αλ) ^(system) is a characteristic of the instrument and φ_(αλ)^(part) is the phase change on reflection for that particularmeasurement location. In the case of bulk materials such as thick metalfilms the surface characterization technique yields a refractive indexcalculated for example using Equation (6). The electronic processor canthen calculate the value of the phase change of reflection for lightreflecting off the metal at various angles of incidences and wavelengthsusing the complex argument of the Fresnel coefficients of reflection.For more complicated surface structures the optimization of the meritfunction in Equation (8) yields the optical properties of the structure.The scattering matrix technique then calculates the phase change ofreflection as a function of angle of incidence and wavelength. Asdescribed above in the profiling analysis section, when a low numericalaperture (NA) interference objective is used for topography measurementsthe correction for the effect of the phase change on reflection amountssimply to subtracting from the surface height the calculated phasechange divided by the wavenumber used for surface height calculation(e.g., as shown in Eq. 16). For high-NA interference objectives thecorrection results from the modeling of the interferometer: the modelsums the interference signals generated by various source points atvarious wavelengths with the appropriate weights for an object point ofheight h=0. The sum interference signal is analyzed with the samealgorithm used for topography measurement and yields an effective heighth′, which is simply the height offset due to the combination of phasechanges on reflection. The value h′ is then subtracted from theexperimental topography map at the locations corresponding to theparticular surface structure.

In another example, the accuracy of the measurement in the ellipsometrymode is improved when the object surface is normal to the optical axisof the interference objective (i.e., there is no tip and tilt of theobject surface relative to the interference objective). This can beaccomplished by having the electronic processor switch to the topographymode and performing repeated measurements of the surface tip and tiltwhile adjusting part orientation. As described above, the procedure canbe automated with a motorized tip/tilt stage 960, which makes theinstrument self aligning. Once the part is properly nulled theinstrument can switch back to the surface characterization mode (e.g.,an ellipsometry mode or a reflectometry mode).

In yet another example, the topography mode of measurement can also beused to measure the surface roughness of a top layer. This informationcan then be included in the ellipsometric model of the surface.Similarly, the topography of the top surface potentially providesinformation about the thickness uniformity of a film. This informationcan be used to best select the size of the field stop that defines themeasurement area in surface characterization mode. For example, one maywant to select a small region where the thickness is nominally constant.

Furthermore, in those embodiments in which a portion of the interferencesignal is selected to isolate a corresponding interface in the testobject, it is possible to measure the film optical thickness or physicalthickness (if the refractive index is known) in the topography mode.This a priori information on thickness can then be fed to the surfacecharacterization mode and provide accurate guess values for theellipsometry model.

Narrow-band Tunable Source

In yet another embodiment, light source 102 in system 100 of FIG. 1 isreplaced by a tunable monochromatic source under the control of theelectronic processor. For example, the source can be a tunable laserdiode or a broadband source incorporating a tunable spectral filter toproduce a tunable spectral output (e.g., a monochromator, a spectralfilter wheel, or a tunable liquid crystal filter.) Furthermore, theposition of reference mirror 122 is adjusted so that the optical pathlength difference between the test light and reference light when thetest surface is in-focus with respect to the interference objective isnon-zero. Detector 134 records the interference pattern produced by thecombined light as the wavelength of the source is scanned. There is nomechanical motion of the object with respect to the interferometricobjective in this case. Because of the adjustment in the position of thereference mirror and the resulting non-zero optical path lengthdifference between the test and reference legs of the interferometer,the scanning of the source frequency produces an interference signalthat is measured at each detector element. This interference signal issometimes referred to as a “channel spectrum.”

When operating in the ellipsometry mode (as in FIG. 1), the intensity ofthe interference signal measured at each detector element corresponds toEq. 4, except that “z” is fixed at the non-zero optical path lengthdifference, and the wavenumber k is varied. During analysis, theelectronic processor determines the wavelength-dependent, complexreflectivity of the test surface from the interference cross-term in Eq.4 using a analytical framework similar to that shown above. For example,the interference signal at each detector element can be Fouriertransformed, filtered to select the portion of the transformed signalcorresponding to the cross-term, and then inversed Fourier transformedto give the magnitude and phase of the signal with respect towavelength. This magnitude and phase can then be related as toellipsometry parameters in a similar fashion to that described above.When operating in the profiling mode (as in FIG. 3), the interferencesignal in the present embodiment can be Fourier transformed, andvariations in the phase at the non-zero optical path length differencecoordinate in the transform over the various detector elements can berelated changes in the topography of the test surface. Information fromthe other coordinates in the Fourier transform can also be analyzed toprovide topography information.

Accordingly, this narrow-band, tunable source embodiment can alsooperate in the various modes of operation and for the variousapplications described above.

Additional Embodiments

The embodiments shown in FIGS. 1 and 3 implement an interferenceobjective of the Mirau-type, in which the beam splitter in theinterference objective directs the reference light back along theoptical axis for the test light. In other embodiments, interferometrysystem 100 can instead use a different type of interference objective,such as a Michelson objective, in which the beam splitter directs thereference light away from the optical axis of the test light (e.g., thebeam splitter can be oriented at 45 degrees to the input light so thetest light and reference travel at right angles to one another). In suchcases, the reference surface can be positioned outside of the path ofthe test light.

In another embodiment, the interference objective can be of theLinnik-type, in which the case the beam splitter is positioned prior tothe objective lens for the test surface (with respect to the inputlight) and directs the test and reference light along different paths. Aseparate objective lens is used to focus the reference light to thereference lens. In other words, the beam splitter separates the inputlight into the test and reference light, and separate objective lensesthen focus the test and reference light to respective test and referencesurfaces. Ideally the two objective lenses are matched to one another sothat the test and reference light have similar aberrations and opticalpaths.

Additional interferometer configurations are also possible. For example,the system can be configured to collect test light that is transmittedthrough the test sample and then subsequently combined with referencelight. For such embodiments, for example, the system can implement aMach-Zehnder interferometer with dual microscope objectives on each leg.

The light source in the interferometer may be any of: an incandescentsource, such as a halogen bulb or metal halide lamp, with or withoutspectral bandpass filters; a broadband laser diode; a light-emittingdiode; a combination of several light sources of the same or differenttypes; an arc lamp; any source in the visible spectral region; anysource in the IR spectral region, particularly for viewing roughsurfaces & applying phase profiling; and any source in the UV spectralregion, particularly for enhanced lateral resolution. For broadbandapplications, the source preferably has a net spectral bandwidth broaderthan 5% of the mean wavelength, or more preferably greater than 10%,20%, 30%, or even 50% of the mean wavelength. For tunable, narrow-bandapplications, the tuning range is preferably broad (e.g., greater than50 nm, greater than 100 nm, or greater than even 200 nm, for visiblelight) to provide reflectivity information over a wide range ofwavelengths, whereas the spectral width at any particular setting ispreferable narrow, to optimize resolution, for example, as small as 10nm, 2 nm, or 1 nm. The source may also include one or more diffuserelements to increase the spatial extent of the input light being emittedfrom the source.

Furthermore, the various translations stages in the system, such astranslation stage 150, may be: driven by any of a piezo-electric device,a stepper motor, and a voice coil; implemented opto-mechanically oropto-electronically rather than by pure translation (e.g., by using anyof liquid crystals, electro-optic effects, strained fibers, and rotatingwaveplates) to introduce an optical path length variation; any of adriver with a flexure mount and any driver with a mechanical stage, e.g.roller bearings or air bearings.

The electronic detector can be any type of detector for measuring anoptical interference pattern with spatial resolution, such as amulti-element CCD or CMOS detector.

Software

The analysis steps described above can be implemented in computerprograms using standard programming techniques. Such programs aredesigned to execute on programmable computers or specifically designedintegrated circuits, each comprising an electronic processor, a datastorage system (including memory and/or storage elements), at least oneinput device, and least one output device, such as a display or printer.The program code is applied to input data (e.g., images from thedetector) to perform the functions described herein and generate outputinformation (e.g., refractive index information, thicknessmeasurement(s), surface profile(s), etc.), which is applied to one ormore output devices. Each such computer program can be implemented in ahigh-level procedural or object-oriented programming language, or anassembly or machine language. Furthermore, the language can be acompiled or interpreted language. Each such computer program can bestored on a computer readable storage medium (e.g., CD ROM or magneticdiskette) that when read by a computer can cause the processor in thecomputer to perform the analysis and control functions described herein.

A number of embodiments of the invention have been described.Nevertheless, it will be understood that various modifications may bemade without departing from the spirit and scope of the invention.

1. Apparatus comprising: an interferometer configured to direct testlight to a test surface and subsequently combine it with reference lightto form an interference pattern, the test and reference light beingderived from a common source; an electronic detector; one or more opticsconfigured to direct at least a portion of the combined light to thedetector so that different regions of the detector correspond todifferent illumination angles of the test surface by the test light; andan electronic processor coupled to the detector, wherein the electronicprocessor is configured to process information measured by the detectorto determine information about a test object having the test surface. 2.The apparatus of claim 1, wherein the test object comprises one or morelayers on a substrate.
 3. The apparatus of claim 1, wherein theelectronic processor extracts angularly resolved reflectivityinformation about the test surface from the detector measurement, anddetermines the information about the test object based on the angularlyresolved information.
 4. The apparatus of claim 1, further comprising atranslation stage configured to adjust the relative optical path lengthbetween the test and reference light when they form the interferencepattern, wherein the electronic processor is configured to analyze aninterference intensity signal measured at each of multiple locationsacross the detector and produced by scanning the translation stage. 5.The apparatus of claim 4, wherein the electronic processor is configuredto determine the correspondence between the different regions of thedetector and the different illumination angles of the test surface bythe test light based on the frequency of the intensity signal atdifferent locations on the detector.
 6. The apparatus of claim 4,wherein the electronic processor is configured to extract angularlyresolved and wavelength-resolved information about the test surfacebased on the intensity signals measured across the detector.
 7. Theapparatus of claim 6, wherein the electronic processor is configured totransform the interference signal at different locations of the detectorinto a frequency domain to extract the angularly resolved andwavelength-resolved information.
 8. The apparatus of claim 7, whereinthe interferometer comprises one or more polarization elementspositioned to adjust the polarization content of the interferencepattern measured by the detector, and wherein the electronic processoris configured to extract angularly resolved, wavelength-resolved, andpolarization-resolved information about the test surface based on theintensity signal measured across the detector.
 9. The apparatus of claim8, wherein the angularly resolved, wavelength-resolved, andpolarization-resolved information is reflectivity information about thetest surface.
 10. The apparatus of claim 1, wherein the informationabout the test object comprises a refractive index estimate for aportion of the test object.
 11. The apparatus of claim 1, wherein theinformation about the test object comprises a thickness estimate for alayer in the test object.
 12. The apparatus of claim 4, wherein theelectronic processor is configured to select a subset of each of theinterference intensity signals, the subsets corresponding to a selectedinterface in the test object, and process the subsets of interferenceintensity signals to determine information about the test object relatedto the selected interface.
 13. The apparatus of claim 1, wherein theelectronic processor is configured to determine the information aboutthe test object based on a comparison between data based on theinformation measured by the detector and a model for the test object.14. The apparatus of claim 13, wherein the model provides an estimatefor the measured information as a function of one or more parameters forthe test object, and wherein the comparison selects values for the oneor more parameters to optimize the fit between the measured informationand that provided by the model.
 15. The apparatus of claim 1, whereinthe electronic processor stores calibration information about theoptical properties of the interferometer and uses the calibrationinformation and the information measured by the detector to determinethe information about the test object.
 16. An interferometry method,comprising: directing test light to a test surface over a range ofillumination angles; subsequently combining the test light withreference light to form an interference pattern, wherein the test andreference light are derived from a common source; directing at least aportion of the combined light to a multi-element detector so thatdifferent elements of the detector correspond to different illuminationangles of the test surface by the test light; and determininginformation about a test object having the test surface based oninterference signals measured by the detector elements.
 17. The methodof claim 16, wherein the combined light is directed to the detector byimaging a pupil plane for the test light to the detector.
 18. The methodof claim 16, further comprising measuring the interference signal ateach of multiple elements of the detector as a function of varying anoptical path length difference between the test and reference light. 19.The method of claim 16, further comprising determining a relationshipbetween different illumination angles of the test surface by the testlight and different elements of the detector based on the frequency ofthe interference signal at each of different detector elements.
 20. Themethod of claim 16, further comprising determining the location of anoptical axis for the combined light on the detector based on thefrequency of the interference signal at different detector elements. 21.The method of claim 18, further comprising determining the rate at whichthe optical path length difference is varied by based on the frequencyof the interference signal at different detector elements.
 22. Themethod of claim 16, wherein the test surface has known reflectionproperties, and the method further comprises calibrating reflectionparameters of an interferometer used to direct the test light andcombine it with the reference light based on a signal measured atdifferent detector elements and the known reflection parameters of thetest surface.
 23. The method of claim 22, further comprising repeatingthe steps with a second test surface having known reflection properties,and further calibrating reflection parameters of the interferometerbased on signals measured at the different detector elements and theknown reflection parameters of the test surfaces.
 24. The method ofclaim 16, wherein the test light, reference light, and combined lightare selectively polarized.
 25. The method of claim 16, whereindetermining the information about the test object comprises determininga reflectivity for the test surface with respect to differentillumination angles and wavelengths.
 26. The method of claim 25, whereinthe reflectivity is a complex reflectivity with respect to the differentillumination angles and wavelengths, for a selected polarization state.27. The method of claim 25, wherein determining the information aboutthe test object further comprises comparing the measured reflectivity toestimate for the reflectivity based on a model of the test object.